Hyenas have been part of the living fabric of Ethiopia for centuries, co-existing with man and domestic animals. Photograph: Andrew McConnell/Alamy

The two hyenas moved into the middle of the backstreet that led to my house – between me and my front gate. I froze like the proverbial rabbit in the headlights: I was on foot, alone, and it was close to midnight on a rainy night in Addis Ababa, Ethiopia's ramshackle capital where I'd recently moved. Nobody was at hand to help or tell me what to do. I was very scared.

This all happened a stone's throw from Bole Avenue, the city's commercial hub. Every day, I'd walk to work across fields dotted with cows accompanied by frog song. And this was the heart of the capital city, in the year 2002. I had, however, moved to the city just as it was on the cusp of radical change: globalisation had reached the country, and Chinese funds too.

The fields I used to walk through next to the airport are today occupied by luxury hotels. This pulsating metropolis of five million people now has a ring road, high rises and malls, and the city is fast losing its patchwork of gardens, streams and village neighbourhoods – and also its hyenas. But back in the early 2000s, it often seemed to me that Addis had perfectly applied Alphonse Allais's tongue-in-cheek answer to urban woes: build a city in the countryside.

Hyenas have always featured prominently in the life of Addis Ababa – and Ethiopia. Contrary to many countries where the beasts are reviled and feared, in Ethiopia there is a long tradition of people and hyenas living side-by-side in harmony. This was brought home to me when I read a recent BBC article saying that hyenas were "out of control" in the Ethiopian capital (up to a 1,000 of them are "running amok" here, apparently), possessing a bite "stronger that a white shark" (quite true) and gobbling up vagrants' and rough sleepers' toes and fingers (a preference for finger food, it seems).

A few voices pointed out the benefits of their increased presence, as "they eat up dangerous stray dogs and are a free clean-up service". But overall – following the news of a baby being snatched straight from its mother's arms – it was a familiar story of the fear of the beast: the wolf baying at the gates of Paris or London in the middle ages, snatching enfants or infants from their cradles.

Addis Ababa is home to 5 million people; if there were 1,000 hyenas 'running amok' they would know about it. Photograph: Jose Cendon/AFP/Getty Images

But the story of Addis Ababa and Ethiopia's long coexistence with hyenas is a more nuanced affair. I would argue there are fewer hyenas in the city itself, and more of the beasts on the periphery. Fewer in the city because ringroads, fast cars and a blanket of cement and urbanisation have erased a lot of the "wild" urban areas. More in the periphery because Addis Ababa has grown so tremendously in the last few years.

People are moving into what were sparsely populated areas, and the increasing wellbeing and economic growth in Ethiopia has led to a tremendous increase in the number of domestic animals being slaughtered, with bones – and all sorts of other solid wastes – being dumped on the outskirts of the capital: more food for scavengers. Far from its drought-prone image, booming Ethiopia has the largest cattle numbers in Africa – and a lot of that cattle finishes on the plates of Addis Ababa's new middle classes.

After moving to the city, I ran a horse trekking outfit a few miles from the capital. I can safely say that Ethiopia and the outskirts of Addis have some of the highest concentrations of hyena in the world. When we put down an old horse in the bottom of the field next to the stables, around 30 hyenas turned up at dusk. In the morning, you would have been hard-pressed to find a single horse hair … that old white-shark bite again. Yet when we walked down to the village through the forest in the evening, and sometimes found ourselves surrounded by hyenas, a quick "shoo!" and these not-so-terrifying beasts would scamper.

In the Entoto Hills, the resting grounds of most of the hyena packs these days, there are hundreds of shepherd children out every day of the year, on their own, without even a dog for protection. The only proven casualty I've heard of in 12 years was a drunken man who was hit by a car – and abandoned unconscious in a pool of blood.

In the eastern Ethiopian city of Harrar, I stood with a hyena on either side and looked on in wonder as their "minder" called them in turn by name, and fed them tidbits from a stick he clenched between his own teeth. A cat looked on through all this, patiently waiting its share of offal. It too had a hyena on either side and seemed unfazed.

A hyena in Addis Ababa. Photograph: Yves Marie Stranger for the Guardian

In Addis, I have now moved to the top of the city, where the city blends into the Entoto Hills' forest. Most nights I can hear the hyenas as I lie in bed, chuckling and snorting – along with the sound of orthodox church sermons and the muezzins' call to prayer, they form a reassuring aural backdrop to everyday life.

Are hyenas tremendous predators? Yes. Are they dangerous? Yes, in certain circumstances; you should certainly not treat them lightly. Do they attack or maim people in Addis Ababa? No, or extremely rarely so – there are certainly less incidents than those involving dogs. Even in Harrar, where hyena are often practically domesticated, cases of attacks on people are just about unheard of.

There again, efforts are now being made to better control solid wastes in the capital, and prevent people from slaughtering their own animals. Paradoxically, if this clean-up is too efficient, suddenly removing vast amounts of the waste that has fed a large increase in hyena numbers around the capital, it could have dangerous consequences.

Another complicating factor is that the once-barren hills around the capital, first planted with eucalyptus, are now being reforested with local indigenous tree species. I have seen Menelik bushbuck, klipspringer, African bush pig, warthog and serval cat in these richer, more diverse woods. (Leopard is also present, though rarely seen – a leopard neatly slaughtered a sheep right next to our stables last year, in broad daylight.) How this will affect the hyena population remains to be seen – hyenas, far from being just scavengers, can be very efficient hunters too.

But are there currently 1,000 hyenas running amok in Addis Ababa? I don't think so. Alphonse Allais's answer to urban woes may no longer be the best fit as the city grows and grows – but I'll miss the hyenas when they blend back into the woods and out of the streets.

I came across two of them a couple of weeks ago as I walked the last stretch of road from the Iyesus church up to my house – and I felt right at home. I had learned not to see myself as a rabbit anymore – and I knew the hyenas didn't see me that way either.